After several back-and-forth emails with Freading's support people in the past couple days, I think I've figured out what happened and why I haven't been able to download any e-books.
Freading recently did a site and app upgrade. From what I can tell, part of that "upgrade" involved making the Freading app the absolutely only way that you can read Freading e-books on mobile devices. Because I didn't have the Freading app installed, the website couldn't find anything to connect with, so it couldn't download and open any e-books.
I have a few choices. 1) I can throw my hands up in the air and stop using Freading, which I don't really want to do. 2) I can adapt to using the Freading app and hope it has all the features I've become accustomed to in Mantano Reader. I'd rather not have to do this, but if I want to read Freading books on my tablet I don't really have a choice right now. 3) I can use this as encouragement to figure out how to download Freading books onto my computer and transfer them to my Simple Touch.
Since one of the main reasons I upgraded Mantano Reader Lite was so that I could use Freading e-books, I'm kind of bummed. I suppose I'll give option 2 a try tonight, since I'm still reading A Lot Like a Lady on my Simple Touch. The recent negative reviews of the Freading app kind of worry me, though.
ETA: And now they're telling me that I'm free to read on any reading app I'd like, as long as it's compatible with their files. Which are EPUB and PDF, both of which Mantano Reader can open. Do they not understand that the Freading site is refusing to communicate with anything but the Freading app? I give up.